The enlargement of the gauge group corresponds to an increase in the
number of fundamental fields of the theory. This increase can be
mitigated by imposing charge conjugation constraints on the
noncommutative gauge action and can be fully avoided by the use of the
Seiberg-Witten map [1]}, that relates the fields in the deformed
action (the “quantum” fields) to the classical fields, in such a way
that the ordinary gauge variations of the classical fields induce the
\(\star \) -gauge variations on the quantum fields. We thus obtain
a gravity theory on noncommutative spacetime with the same
degrees of freedom as classical gravity.
